I think some MBs do and some don't.
I think it would depend on the BIOS code....or perhaps they default to full speed until the BIOS takes over.
I've had motherboards that do it and motherboards that don't.
I'd replace the fan...the bearings sound like they're failing.
I always understood that this is always done at the beginning of the POST process on any mobo, and the purpose is to ensure that the fan DOES start before being slowed down to whatever is required. However, I am NOT sure this is always done if you choose NOT to let the automatic system exercise control. IF you have chosen to run that fan at a fixed slow speed for noise reduction (also reduces cooling, of course), on some mobos it may NOT use that full-speed first start-up option. In those cases it is YOUR responsibility to arrange to ensure start-up.
I made no changes to this mobo fan control. I found a fan power port that ran the fan at around 700 RPM. I then used a fan cable with a resistor that slowed it to around 550 rpm. When I saw the fan fail to start once, I changed the fan cable so it runs at around 650 rpm and I've not seen it fail to start since.
These fans are fairly quiet at most speeds. I'm not a gamer, I just like cool quiet computers. The faster the fans run, the quicker they wear out, although these fans usually last over ten years. The faster the case fans run, the more air they pull in, and the quicker the air filters load up with dust.
I always thought that the BIOS is late at loading the fan settings hence, why the fan spins at max RPM from cold booting.
Since BIOS is based on per mobo manufacturer, then maybe some mobo manufacturers have figured out a way to instantly load fan settings.
The faster the fans run, the quicker they wear out, although these fans usually last over ten years.